00 / Premise
Many of the most consequential scientific questions are inverse problems: we observe incomplete, indirect, and noisy measurements, then seek to recover the hidden physical systems that produced them. In geophysics, the unknown may be the structure of the subsurface. In computational imaging, it may be an object or field that cannot be measured directly. Across these domains, the central difficulty is the same: the data are limited, the forward physics are expensive, and many plausible explanations can fit the observations.
I see scientific machine learning as a way to change how these problems are formulated—not by replacing mathematical or physical reasoning with generic prediction, but by connecting regularization theory, optimization, uncertainty, numerical analysis, learning, and simulation in a unified computational framework. My agenda is centered on algorithms whose behavior can be studied theoretically and tested at the scale of real geophysical systems.
01 / Current trajectory
From geophysical applications to general methods
The agenda grows from verified work in seismic acquisition, denoising, mineral prospectivity, and geospatial AI.
02 / Recurring themes
A coherent trajectory
Across problems and modalities, four questions repeatedly organize the work.
Learning under incomplete information
Subsurface observations and scientific images are rarely complete. Acquisition is constrained by cost, geometry, access, and noise. A recurring theme in my work is how to recover useful structure from sparse or imbalanced information without allowing the learned model to invent unsupported detail.
Mathematical and physical structure as algorithmic resources
Forward operators, stability, identifiability, acquisition geometry, governing equations, geological context, and known invariances are not merely constraints applied after training. They determine representations, objectives, regularizers, uncertainty models, and optimization strategies.
Co-designing measurement and reconstruction
The quality of an inverse solution depends on what is measured as much as on how it is reconstructed. This motivates a unified view of experimental design, sensing geometry, forward simulation, and inversion rather than treating them as separate stages.
Methods that survive scientific scale
A method is scientifically useful only if it can operate at the scale and fidelity of the physical system. Large models, three-dimensional domains, multiple physical modalities, and repeated forward solves make computational efficiency a first-class research question.
Central research question
How can mathematical structure, physical knowledge, and learned representations be combined to produce inverse methods that are stable, identifiable, uncertainty-aware, and scalable enough for scientific discovery?
03 / Research agenda
Four connected research pillars
Each pillar addresses a different layer of the same problem: how to make learning-based scientific inference trustworthy and useful at scale.
Mathematical foundations for learned inverse problems
Study identifiability, stability, regularization, and uncertainty when learned representations interact with structured forward operators and incomplete observations.
- Connect classical regularization theory with learned priors and data-consistency operators.
- Characterize when mathematical and physical structure improve identifiability, robustness, and transfer.
- Develop uncertainty descriptions that distinguish observational ambiguity from model and prior error.
Optimization for coupled sensing and reconstruction
Treat acquisition design and inversion as a coupled optimization problem so that measurements are selected for the scientific question they must ultimately answer.
- Optimize sensor placement and acquisition geometry jointly with reconstruction objectives.
- Develop bilevel, constrained, and differentiable optimization methods for experimental design.
- Balance reconstruction quality, uncertainty, computational cost, and field constraints.
Reliable computational imaging with limited data
Create methods that distinguish recoverable information from learned assumptions when observations are sparse, noisy, or drawn from changing distributions.
- Combine model-based reconstruction with data-adaptive regularization.
- Measure sensitivity to noise, sampling geometry, prior mismatch, and distribution shift.
- Build uncertainty and failure detection into the reconstruction pipeline rather than adding them afterward.
Large-scale scientific computing for learned physics
Make physics-informed learning practical for three-dimensional, multiphysics, and high-resolution problems through algorithms designed around modern computing systems.
- Reduce the memory and compute required by differentiable simulation and repeated inverse solves.
- Explore operator learning, multiscale methods, domain decomposition, and structure-aware surrogates.
- Design reproducible implementations that connect methodological advances with real scientific workflows.
04 / Near-term program
Questions that can be tested now
A long-term agenda becomes credible through falsifiable questions, explicit evaluation, and reproducible evidence.
Identifiability
Determine when learned priors improve an inverse solution and when they merely produce plausible but unsupported structure.
Evaluation
Evaluate data consistency, sensitivity to prior mismatch, and uncertainty under controlled changes in sampling and noise.
Experimental design
Co-optimize sensing geometry and reconstruction so that measurements are selected for the scientific quantity of interest.
Evaluation
Compare bilevel and differentiable design strategies against fixed geometries under physical and operational constraints.
Scientific scale
Reduce the computational burden of learned inverse methods in three-dimensional and multiphysics settings.
Evaluation
Study multiscale solvers, operator surrogates, and memory-aware differentiation using reproducible computational benchmarks.
05 / Application focus
Computational geophysics as a proving ground
Computational geophysics provides an unusually demanding environment for this agenda. The forward processes are governed by rich physics; observations are indirect and expensive; spatial scales vary dramatically; and the consequences of uncertainty matter. Seismic, electromagnetic, gravity, magnetic, and geological data also offer opportunities to study how multiple sensing modalities can constrain a shared physical model.
I intend to use geophysical inverse problems not as isolated applications, but as rigorous testbeds for broadly useful ideas in computational imaging and scientific machine learning. Methods developed under these constraints can inform other domains where hidden structure must be inferred from limited physical measurements.
06 / Principles
Methodological commitments
Theory and computation together
Theoretical questions about stability, identifiability, convergence, and approximation should inform algorithms—and computational experiments should expose where theory needs to become sharper.
Physics before plausibility
A visually convincing reconstruction is not necessarily a physically supported one. Evaluation must include consistency with measurements and governing models.
Uncertainty as an output
Inverse methods should communicate ambiguity, sensitivity, and failure modes—not only return a single estimate.
Scale as part of the method
Computational complexity, memory, parallelism, and data movement should shape algorithm design from the beginning.
Reproducibility as research infrastructure
Open implementations, controlled benchmarks, and transparent comparisons are necessary for progress across disciplines.
07 / Long-term horizon
From predictive models to dependable instruments of scientific inference
The long-term outcome I seek is a new class of scientific computing systems in which simulation, sensing, learning, and inversion are designed together. Such systems would use data efficiently, respect known physics, adapt across scales, and expose uncertainty in forms that scientists can interrogate.
This agenda sits at the intersection of machine learning, optimization, computational imaging, and high-performance scientific computing. It is intentionally methodological and interdisciplinary: the goal is to contribute foundational algorithms while remaining accountable to real physical problems. Ultimately, I want to help make machine learning a dependable instrument for scientific inference—not simply a mechanism for prediction.